The built-in flash will fire but what is happening is that while the shutter is still closed it is sending out brief flashes of light to instruct the off-camera flash - sort of a light Morse code. When this is finished the shutter will open then the built-in flash will wink to trigger the off-camera flash. The wink is a very low power flash and doesn't contribute a significant amount of light to the scene.

As kgbruce01 says, sometimes you want to use the off-camera flash as the main light and the built-in flash as a fill light. You do this by assigning the two flashes to different groups with different ± stop values. The built-in flash would typically be set between -1.0 and -2.0 stops when used as a fill light, but of course that value can be higher or lower as desired.

I can get over the built-in flash not going off, I wasn't intending to use it anyway until someone advised me to let it be a fill light. I just really need that off-camera flash to go off and it's not happening.

Maybe I'm just being slow, but I'm still not seeing any directions for how to actually sync them and make it so that the built-in flash can actually trigger it. I had the sync cord plugged into the D5100'S mic jack, in the same area where you would plug it into a computer to transfer pictures, with the other end plugged into the hot shoe I attached to the SB700 (but the flash seems really loose/unstable on it, but I can't push it in further). This setup failed to sync them, with the SB700 set to Remote- but I didn't do any other settings because I don't know what any of them mean in this situation. So idk if I was supposed to press certain buttons or what.

Somebody said that the sync cord needs to be plugged into the hot shoe on both ends- which prevents the built-in flash from popping up all the way on the D5100. Am I damaging the camera by putting something in a place that prevents another part from working properly? And can the built-in flash actually function when it isn't raised up completely? The only function I need from the built-in flash is to trigger the OCF, I don't mind if it's not going to contribute to the exposure. I just need the OCF to actually go off when I hit the shutter.

All I need to know is how to make it so that the SB700, being used off-camera, goes off when I hit the shutter on the D5100. Like exactly what pieces to put where, what buttons to press if any are necessary... Sorry if I'm wording it weirdly and confusing people, or just misunderstanding answers myself.

I bought the OCF starter kit recommended by Strobist, and it came with a sync cord and 2 hot shoe units.